Fundamental Theorem of Calculus

.I can find antiderivatives.

.I can use the Fundamental Theorem of Calculus.

​A function F is called the antiderivative of the function f on an interval I if F′ (x)=f(x) for every value of x in I.

​The expression F(x)+C is called the general antiderivative of f since it generalizes the family of antiderivatives of f.

​The process of finding all antiderivatives of f(x) is called antidifferentiation. The other term used for this process is integration, and we also call an antiderivative an integral of f.

​The symbol ∫, called the integral sign, is used to denote the integral of a function. The integral of f(x) can be written as:

  ∫f(x)dx=F(x)+C

​the basic formula for integration can be derived from the differentiation formulas.

Let us introduce some of the basic formulas​